Display length of object to render, dynamically
We can use a frame change handler to alter the text objects content before each frame during playback.

import bpy

def distance(p1, p2):
    return sqrt((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2+ (p1[2]-p2[2])**2)

def update_size(scene):
    point1 = scene.objects['Empty.001'].location
    point2 = scene.objects['Empty.002'].location
    scene.objects['Text'].data.body = '{:.3f}'.format(distance(point1, point2))

bpy.app.handlers.frame_change_pre.append(update_size)

# to disable
# bpy.app.handlers.frame_change_pre.remove(update_size)


Instead of using distance between two points you may prefer to add the length of the pose bones between shoulder and hand.

format(scene.objects['rig'].pose.bones['upper_arm.L'].length +
        scene.objects['rig'].pose.bones['forearm.L'].length)